Great project! I'm also maintaining a fully in-browser data visualisation/analytics tool [1] and I often found it hard to convince people that their data isn't sent anywhere. It's funny I also say the exact same thing that they can inspect the Network tab. As a potential alternative to open-sourcing the codebase, maybe a desktop version of the same tool (i.e. an Electron app) could help address the privacy concerns if it explicitly states that it won't make network calls, although it's a perception problem rather than a technical one.
[1]: https://docs.visprex.com/